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Geometric frustration and compatibility conditions for two dimensional director fields
Idan Niv,Efi Efrati +1 more
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TLDR
This work establishes the necessary and sufficient conditions for two scalar functions, s and b, to describe the splay and bend of a director field in the plane, generalizes these compatibility conditions for geometries with non-vanishing constant Gaussian curvature, and provides a reconstruction formula for the director field depending only on the s play and bend fields and their derivatives.Abstract:
The uniform director field obtained for the nematic ground state of the hard-rod model of liquid crystals in two dimensions reflects the high symmetry of the constituents of the liquid; It is a manifestation of the constituents' local tendency to avoid splaying and bending with respect to one another. In contrast, bent-core (or banana shaped) liquid-crystal-forming-molecules locally favor a state of zero splay and constant bend. However, such a structure cannot be realized in the plane and the resulting liquid-crystalline phase is frustrated and must exhibit some compromise of these two mutually contradicting local intrinsic tendencies. The generation of geometric frustration from the intrinsic geometry of the constituents of a material is not only natural and ubiquitous but also leads to a striking variety of morphologies of ground states and exotic response properties.
In this work we establish the necessary and sufficient conditions for two scalar functions, $s$ and $b$ to describe the splay and bend of a director field in the plane. We generalize these compatibility conditions for geometries with non-vanishing constant Gaussian curvature, and provide a reconstruction formula for the director field depending only on the splay and bend fields and their derivatives. Last, we discuss optimal compromises for simple incompatible cases where the locally preferred values of the splay and bend cannot be globally achieved.read more
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Interpretation of saddle-splay and the Oseen-Frank free energy in liquid crystals
TL;DR: In this paper, the authors re-examine a classic question in liquid-crystal physics: What are the elastic modes of a nematic liquid crystal? The analysis uses a recent mathematical construction, which br...
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Twist renormalization in molecular crystals driven by geometric frustration
TL;DR: The theory provides a mechanism for the conveyance of twist across length-scales observed experimentally and reconciles the apparent paradox of a twisted single crystal as a finite size effect.
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Uniform distortions and generalized elasticity of liquid crystals.
TL;DR: A definition of uniform distortion is given which makes precise the intuitive notion of seeing everywhere the same director landscape, and it is proved that all such distortions fall into two families, each described by two scalar parameters.
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Evolving, complex topography from combining centers of Gaussian curvature
TL;DR: This work employs a generalized metric compatibility condition to characterize two families of interfaces between circular director patterns, hyperbolic and elliptical interfaces, and finds that the deformed interfaces are geometrically compatible.
References
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Piezoelectric Effects in Liquid Crystals
TL;DR: In this paper, a theory of the relationship between curvature strains and electric polarization in liquid crystals is developed in analogy to piezoelectric theory in ordinary crystals, which may explain some recently observed phenomena in nematic liquid crystals.
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Bent-Core Liquid Crystals: Their Mysterious and Attractive World
Hideo Takezoe,Yoichi Takanishi +1 more
TL;DR: In this article, structural and properties of liquid crystalline phases formed by bent-core molecules are reviewed and the most attractive properties of this new class of liquid crystals are in polarity and chirality, despite being formed from achiral molecules.
Journal ArticleDOI
Geometry and Mechanics in the Opening of Chiral Seed Pods
TL;DR: The theoretical analysis quantitatively predicts all observed configurations, thus linking the pod’s microscopic structure and macroscopic conformation and suggesting that this type of incompatible strip is likely to play a role in the self-assembly of chiral macromolecules and could be used for the engineering of synthetic self-shaping devices.
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Nematic twist-bend phase with nanoscale modulation of molecular orientation
Volodymyr Borshch,Young-Ki Kim,Jie Xiang,Min Gao,Antal Jakli,Vitaly P. Panov,Jagdish K. Vij,Corrie T. Imrie,Maria-Gabriela Tamba,Georg H. Mehl,Oleg D. Lavrentovich +10 more
TL;DR: This work experimentally demonstrates a new nematic order, formed by achiral molecules, in which the director follows an oblique helicoid, maintaining a constant oblique angle with the helix axis and experiencing twist and bend.
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